1. About Scilab

Scilab is a freely distributed open source scientific software package,
first developed by researchers from INRIA and ENPC, and now by the Scilab Consortium.
It is similar to Matlab, which is a commercial product.
Yet it is almost as powerful as Matlab. Scilab consists of three main components:

an interpreter

libraries of functions (Scilab procedures)

libraries of Fortran and C routines

Scilab is specialized in handling matrices (basic matrix manipulation, concatenation,
transpose, inverse, etc.) and numerical computations.
Also it has an open programming environment that
allows users to create their own functions and libraries.

2. Installing and Running Scilab

First, you must have the software. Go to the download section in the Scilab homepage,
find a right version for your operating system (platform), and then click to download.
For easy installation, it is advisable to download the installer (for binary version).
Then double click the downloaded file and follow the instructions to complete the installation.

To run Scilab, type

scilex

in the command prompt in the folder bin under the installation directory,
or click the shortcut in the start menu if you use Windows. To exit the program, type

exit

or close the window of the main program.

3. Documentation and Help

To find the usage of any function, type

help function_name

For example:

help sum

If you want to find functions that you do not know,
you may just type

help

and search for the keywords of the functions.
Finally, if you want more information, you may visit the Scilab homepage.
There is a section called documentation.
It is very resourceful.

4. Scilab Basics

Common Operators

Here is a list of common operators in Scilab:

+

addition

-

subtraction

*

multiplication

/

division

^

power

'

conjugate transpose

Common Functions

Some common functions in Scilab are:

sin, cos, tan, asin, acos, atan, abs, min, max, sqrt, sum

E.g., when we enter:

sin(0.5)

then it displays:

ans =
0.4794255

Another example:

max(2, 3, abs(-5), sin(1))
ans =
5

Special Constants

We may wish to enter some special constants like, i (sqrt(-1))
and e. It is done by entering

%pi %i %e

respectively. There are also constants

%t %f

which are Boolean constants representing true and false,
respectively. Boolean variables would be introduced later.

The Command Line

Multiple commands, separated by commas, can be put on the same command line:

A = [1 2 3], s = tan(%pi/4) + %e
A =
1. 2. 3.
s =
3.7182818

Entering a semi-colon at the end of a command line suppresses showing the result
(the answer of the expression):

A = [1 2 3]; s = tan(%pi/4) + %e;

Here the vector [1 2 3] is stored in the variable A,
and the expression tan(%pi/4) + %e is evaluated and stored in
s, but the results are not shown on the screen.

A long command instruction can be broken with line-wraps by using the ellipsis
(...)
at the end of each line to indicate that the command actually continues on the next line:

For example, to enter a 3 x 3 magic square and assign to the variable
M :

M = [8 1 6; 3 5 7; 4 9 2]
M =
8. 1. 6.
3. 5. 7.
4. 9. 2.

Calculating Sums

For a magic square, we may wish to check for its column sums and row sums and the sum of diagonals.
This is done by entering:

sum(M,'c') // column sums
ans =
15.
15.
15.

sum(M,'r') // row sums
ans =
15. 15. 15.

The sum of the main diagonal is easily done with the help of the function
diag.

diag(M)
ans =
8.
5.
2.

Subscripts

It is a bit more difficult to find the sum of the other diagonal.
We will show two ways to accomplish it. One method is to find the sum manually,
i.e., to read the specified elements and then to sum them up.

M(1,3) + M(2,2) + M(3,1)
ans =
15.

It is possible to access elements in a matrix using a single index.
This by treating a matrix as a long vector formed by stacking up the columns of the matrix.
E.g., the values of M(1), M(2),
M(3), M(4), M(5)
are 8, 3, 4, 1, 5, respectively.

Accessing out-of-bound elements will result in an error, like entering:

M(3,4)
!--error 21
invalid index

A smarter way to get the sum of the other diagonal is to use the function
mtlb_fliplr, where mtlb stands for
Matlab. This is to flip a matrix left-to-right (lr):

mtlb_fliplr(M)
ans =
6. 1. 8.
7. 5. 3.
2. 9. 4.

The desired result would then be obtained by typing
sum(diag(mtlb_fliplr(M))).

The Colon Operator

The colon operator is one of the most important operators in Scilab.
The expression 1:10 results in a row matrix with
elements 1, 2, ..., 10, i.e.:

1:10
ans =
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

To have non-unit spacing we specify the increment:

10 : -2 : 2
ans =
10. 8. 6. 4. 2.

Notice that expressions like 10:-2:1, 10:-2:0.3 would produce the same result while 11:-2:2 would not.

The operator $, which gives the largest value of an index,
is handy for getting the last entry of a vector or a matrix.
For example, to access all elements except the last of the last column,
we type:

M(1:$-1, $)

We sometimes want a whole row or a column.
For example, to obtain all the elements of the second row of M,
enter:

M(2,:)
ans =
3. 5. 7.

Now we have a new way to perform operations like mtlb_fliplr(M).
It is done by entering M(:, $:-1:1).
However the function mtlb_fliplr(M) would obtain result faster (in computation time) than using the subscript expression.

Remember that it is an error to access out-of-bound element of a matrix. However,
it is okay to assign values to out-of-bound elements. The result is a larger size matrix
with all unspecified entries 0:

M = matrix(1:6, 2, 3); M(3,1) = 10
M =
1. 3. 5.
2. 4. 6.
10. 0. 0.

It is remarked that this method is slow. If the size of the matrix is known beforehand, we should use pre-allocation:

Deleting Rows and Columns

A pair of square brackets with nothing in between represents the empty matrix.
This can be used to delete rows or columns of a matrix.
To delete the 1st and the 3rd rows of a 4x4 identity matrix, we type:

A = eye(4,4);
A([1 3],:) = []
A =
0. 1. 0. 0.
0. 0. 0. 1.

If we delete a single element from a matrix, it results in an error, e.g.:

A(1,2) = []
!-error 15
submatrix incorrectly defined

If we delete elements using single index expression, the result would be a column vector:

B=[1 2 3; 4 5 6];
B(1:2:5)=[]
B =
4.
5.
6.

Matrix Inverse and Solving Linear Systems

The command inv(M) gives the inverse of the matrix
M. If the matrix is badly scaled or nearly singular,
a warning message will be displayed:

Another method is to type inv(A) * b.
Although it gives the same result, it is slower than A\b
because the first method mainly uses Gaussian Elimination
which saves some computation effort.
Please read the Scilab help file for more details about the slash operator
when A is non-square.

A / b solves for x in the equation
xb = A.

Entry-wise operations, Matrix Size

To add 4 to each entry of a matrix M,
using M + 4 * ones(M) is correct but troublesome.
Indeed this can be done easily by M + 4.
Subtraction of a scalar from a matrix entry-wise is done similarly.

Multiplying 2 to the second column and 3 to the third column of M
can be achieved by using the entry-wise multiplication operator .* :

6. The Programming Environment

Creating Functions

Scilab has an open programming environment that enables users to build their own functions
and libraries. It is done by using the built-in editor SciPad.
To call the editor, type scipad() or editor(),
or click Editor at the menu bar.

The file extensions used by scilab are .sce and .sci.
To save a file, click for the menu File and choose Save.
To load a file, choose Load under the same menu.
To execute a file, type

exec('function_file_name');

in the command line, or click for load into Scilab under the menu
Execute.

To begin writing a function, type:

function [out1, out2, ...] = name(in1, in2, ...)

where function is a keyword that indicates the start of a function,
out1, out2 and
in1, in2, ..., are variables that are
outputs and inputs, respectively, of the function;
the variables can be Boolean, numbers, matrices, etc.,
and name is the name of the function.
Then we can enter the body of the function. At the end, type:

endfunction

to indicate the end of the function.

Comment lines begin with two slashes //.
A sample function is given as below:

A Scilab function can call upon itself recursively.
Here is an example.

Unlike Matlab, Scilab allows multiple function declaration
(with different function names) within a single file.
Also Scilab allows overloading (it is not recommended for beginners).
Please refer to the chapter overloading in its help file for details.

Flow Control

A table of logical expressions is given below:

==

equal

~=

not equal

>=

greater than or equal to

<=

less than or equal to

>

greater than

<

less than

~

not

If a logical expression is true,
it returns a Boolean variable T (true), otherwise
F (false).

The if statement

It has the basic structure:

if conditionbody
end

The body will be executed only when the condition statement is true.
Nested if statements have the structure:

The break and continue commands

They are for ending a loop and to immediately start the next iteration, respectively.
For example:

// user has to input 10 numbers and for those which
// are integers are summed up, the program are
// prematurely once a negative number is entered.
// It is not well written but just to illustrate the
// use of the "break" and "continue" commands
result = 0;
for i = 1:10
tem = input('please input a number');
if tem < 0
break;
end
if tem ~= int(tem) //integral part
continue;
end
result = result + tem;
end
disp(result);

Some Programming Tips

The concept of Boolean vectors and matrices is important. The function
find is useful too.
It reports the indices of true Boolean vectors or matrices. For example:

M = [-1 2; 4 9]; M > 0
ans =
F T
T T
M(M > 0)'
ans =
4. 2. 9.
end

In contrast,

find(M > 0)
ans =
2. 3. 4.
M(find(M>0))'
ans =
4. 2. 9.

We remark that M(M>0) gives results quicker than
M(find(M>0) because the find
function is not necessary here.

It is important to distinguish & and and,
| and or.
The first one of each pair is entry-wise operation
and the other one reports truth value based on all entries of a Boolean matrix.

Debugging

The most tedious work in programming is to debug. It can be done in two ways: either using
Scilab's built-in debugger, or modifying the program so that it serves the same purpose as
a debugger.

The Scilab debugger is similar to those debuggers in other programming languages and is
simple to use.
We present the second method to offer programmers greater flexibilities when debugging.

To insert breakpoints we use

pause

To end pause we use

abort

To set the output of the function we may use

return

To display variables we use

disp (variable)

For details please read the Scilab documentation.

7. Plotting Graphs

2D Graphs

The plot function has different forms, depending on the input arguments.
If y is a vector, plot(y) produces a
piecewise linear graph of the elements of y versus the index of the elements of y.
When x and y are vectors of the same length,
plot(x,y) produces a graph
of y versus x. E.g., to plot the value of the sine function from zero to 2 pi:

t = (0:1/100:2) * %pi;
y = sin(t);
plot(t,y);

3D Surfaces

The command plot3d(x,y,z) plots 3D surfaces.
Here x and y (x-axis and y-axis coordinates)
are row vectors of sizes n1 and n2,
and the coordinates must be monotone, and z is a matrix of size
n1xn2 with z(i,j) being
the value (height) of the surface at the point (x(i),y(j)).